Giải phương trình: \(8\left(x+\dfrac{1}{x}\right)^2+4\left(x^2+\dfrac{1}{x^2}\right)-4\left(x^2+\dfrac{1}{x^2}\right)\left(x+\dfrac{1}{x}\right)^2=\left(x+4\right)^2\)
Giải hệ phương trình
a. \(\left\{{}\begin{matrix}\dfrac{1}{2}\left(x+2\right)\left(y+3\right)-\dfrac{1}{2}xy=50\\\dfrac{1}{2}xy-\dfrac{1}{2}\left(x-2\right)\left(y-2\right)=32\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}\dfrac{3x+5}{x+1}-\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5y+9}{y+4}=9\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}x^2+y^2-2x-2y-23=0\\x-3y-3=0\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}\left(x-y\right)^2-3x-3y=4\\2x+y=3\end{matrix}\right.\)
giải hệ phương trình:
a)\(\left\{{}\begin{matrix}\dfrac{x+1}{x-1}+\dfrac{3y}{y+2}=7\\\dfrac{2}{x-1}-\dfrac{5}{y+2}=4\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}2\left(x^2-2x\right)+\sqrt{y+1}=0\\3\left(x^2-2x\right)-2\sqrt{y+1}=-7\end{matrix}\right.\)
giải hệ sau bằng phương pháp thế
a)\(\left\{{}\begin{matrix}2x-y=4\\x+5y=3\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}-2x+3y=-1\\x+2y=3\end{matrix}\right.\)
giải hệ sau:
a)\(\left\{{}\begin{matrix}x+y=-1\\2x+y=1\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{5}\\\dfrac{3}{x}+\dfrac{4}{y}=2\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}2\dfrac{5}{x-1}+\dfrac{3}{3y-2}=1\\\dfrac{2}{2x-1}+\dfrac{1}{3y-2}=1\end{matrix}\right.\)
Giải các hệ phương trình sau:
a) \( \left\{{}\begin{matrix}x\sqrt{5}-\left(1+\sqrt{3}\right)y=1\\\left(1-\sqrt{3}\right)x+y\sqrt{5}=1\end{matrix}\right.;\)
b) \(\left\{{}\begin{matrix}\dfrac{2x}{x+1}+\dfrac{y}{y+1}=\sqrt{2}\\\dfrac{x}{x+1}+\dfrac{3y}{y+1}=-1\end{matrix}\right..\)
Giải các hệ phương trình :
a) \(\left\{{}\begin{matrix}\left(x+3\right)\left(y+5\right)=\left(x+1\right)\left(y+8\right)\\\left(2x-3\right)\left(5y+7\right)=2\left(5x-6\right)\left(y+1\right)\end{matrix}\right.\);
b) \(\left\{{}\begin{matrix}\dfrac{2x-3}{2y-5}=\dfrac{3x+1}{3y-4}\\2\left(x-3\right)-3\left(y+2\right)=-16\end{matrix}\right.\).
1. Giải hệ phương trình sau:
\(\left\{{}\begin{matrix}\left(a+b\right)^2=10+2ab\\\left(a+b\right)\left(a-\dfrac{2}{ab}\right)=\dfrac{4}{3}\end{matrix}\right.\)
2.Giải phương trình:
\(\sqrt{\sqrt{2}-1-x}+\sqrt[4]{x}=\dfrac{1}{\sqrt[4]{2}}\)
Cho biểu thức P=\(\left(\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right)\times\left(\dfrac{1}{2\sqrt{x}}-\dfrac{\sqrt{x}}{2}\right)^2\)
a Rút gọn P
b Tìm x để \(\dfrac{P}{\sqrt{x}}>2\)
Tìm tất cả bộ ba số x,y,z thoả mãn:
\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{2}{y}+\dfrac{3}{z}=1\\\dfrac{12}{yz}-\dfrac{1}{x^2}=1\end{matrix}\right.\)
